Displaying similar documents to “Henstock-Kurzweil type integrals in p -adic harmonic analysis.”

The AP-Denjoy and AP-Henstock integrals revisited

Valentin A. Skvortsov, Piotr Sworowski (2012)

Czechoslovak Mathematical Journal

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The note is related to a recently published paper J. M. Park, J. J. Oh, C.-G. Park, D. H. Lee: The AP-Denjoy and AP-Henstock integrals. Czech. Math. J. 57 (2007), 689–696, which concerns a descriptive characterization of the approximate Kurzweil-Henstock integral. We bring to attention known results which are stronger than those contained in the aforementioned work. We show that some of them can be formulated in terms of a derivation basis defined by a local system of which the approximate...

Variational measures related to local systems and the Ward property of 𝒫 -adic path bases

Donatella Bongiorno, Luisa Di Piazza, Valentin A. Skvortsov (2006)

Czechoslovak Mathematical Journal

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Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a 𝒫 -adic path system that defines a differentiation basis which does not possess Ward property.

Kurzweil-Henstock type integral on zero-dimensional group and some of its applications

Valentin Skvortsov, Francesco Tulone (2008)

Czechoslovak Mathematical Journal

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A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.